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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 10 Oct 2015 13:21:18 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/10/t1444479766scc8mlgrcwzx3mp.htm/, Retrieved Tue, 14 May 2024 22:00:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282175, Retrieved Tue, 14 May 2024 22:00:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2015-10-02 20:20:26] [102949d3707834b83d58a354234a805f]
- RMP     [Central Tendency] [] [2015-10-10 12:21:18] [7e1e09e1787c74b32ad6066a9a323b17] [Current]
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Dataseries X:
92.44
94.36
93.42
92.97
94.83
91.47
88.42
86.36
86.01
87.87
89.81
88.41
86.33
89.64
89.53
88.3
99.49
98.81
90.97
92.58
92.98
95
92.47
88.65
84.81
88.6
89.31
92.34
91.53
96.95
95.44
89.59
89.86
91.66
92.7
90.54
86.17
89.15
89.73
91.07
93.36
96.27
95
94.72
97.16
100.92
98.66
95.87
94.6
98.41
98.05
99.82
106.96
107.45
100.25
99.28
101.38
101
97.43
95.38
95.17
94.13
96.43
105.38
98.39
99.8
94.43
90.16
85.49
90.57
88.22
89.66




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282175&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282175&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282175&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean93.616250.597470196135299156.687732050153
Geometric Mean93.4831857082099
Harmonic Mean93.3523621929925
Quadratic Mean93.7515182765947
Winsorized Mean ( 1 / 24 )93.61888888888890.593391210039065157.769254591293
Winsorized Mean ( 2 / 24 )93.58944444444450.577392548685332162.089802955613
Winsorized Mean ( 3 / 24 )93.42944444444450.534460658950609174.810704735292
Winsorized Mean ( 4 / 24 )93.41722222222220.528425378980897176.78413251533
Winsorized Mean ( 5 / 24 )93.413750.526913438261151177.284812299097
Winsorized Mean ( 6 / 24 )93.483750.493926589328353189.266486194072
Winsorized Mean ( 7 / 24 )93.47597222222220.480660517260345194.473997479581
Winsorized Mean ( 8 / 24 )93.48263888888890.478885557184708195.208724686663
Winsorized Mean ( 9 / 24 )93.45763888888890.469691383587079198.976694388438
Winsorized Mean ( 10 / 24 )93.42986111111110.464254180565725201.247215474205
Winsorized Mean ( 11 / 24 )93.38555555555560.447588473558379208.641555965751
Winsorized Mean ( 12 / 24 )93.36888888888890.442093670614763211.197072238226
Winsorized Mean ( 13 / 24 )93.41402777777780.421289410731822221.733623960565
Winsorized Mean ( 14 / 24 )93.441250.416246780805929224.485219607178
Winsorized Mean ( 15 / 24 )93.416250.398152936025306234.624039025202
Winsorized Mean ( 16 / 24 )93.29180555555560.37427066929734249.262935112448
Winsorized Mean ( 17 / 24 )93.23986111111110.36280707101271256.995710835649
Winsorized Mean ( 18 / 24 )93.19236111111110.354188468981267263.115175316563
Winsorized Mean ( 19 / 24 )93.07361111111110.33152858294997280.740834720596
Winsorized Mean ( 20 / 24 )93.05138888888890.322078193149076288.909311056087
Winsorized Mean ( 21 / 24 )92.94930555555560.303884818698729305.870184478368
Winsorized Mean ( 22 / 24 )92.90958333333330.273349538445251339.892958524026
Winsorized Mean ( 23 / 24 )93.01180555555560.253910521002225366.317256915638
Winsorized Mean ( 24 / 24 )92.95180555555560.243444354246692381.81951618136
Trimmed Mean ( 1 / 24 )93.54442857142860.567503363630067164.835020488806
Trimmed Mean ( 2 / 24 )93.46558823529410.536277465364209174.285876755641
Trimmed Mean ( 3 / 24 )93.39803030303030.509223972856078183.412477184038
Trimmed Mean ( 4 / 24 )93.386250.497132327047073187.849884063479
Trimmed Mean ( 5 / 24 )93.37725806451610.484750486137362192.629529489644
Trimmed Mean ( 6 / 24 )93.36850.47017437713603198.582705779789
Trimmed Mean ( 7 / 24 )93.34465517241380.461770457004041202.145143234222
Trimmed Mean ( 8 / 24 )93.32053571428570.454672739425632205.247703726802
Trimmed Mean ( 9 / 24 )93.29351851851850.446075922551042209.142690295829
Trimmed Mean ( 10 / 24 )93.26826923076920.43732921434084213.267868169628
Trimmed Mean ( 11 / 24 )93.2450.42739813203301218.168946028052
Trimmed Mean ( 12 / 24 )93.22583333333330.418423547815405222.802549761042
Trimmed Mean ( 13 / 24 )93.20717391304350.407947692848996228.478247449103
Trimmed Mean ( 14 / 24 )93.18113636363640.398817122023545233.643771086978
Trimmed Mean ( 15 / 24 )93.14928571428570.387651793783837240.291125200437
Trimmed Mean ( 16 / 24 )93.117250.376909155126204247.054890372246
Trimmed Mean ( 17 / 24 )93.09657894736840.368145611830522252.879773534353
Trimmed Mean ( 18 / 24 )93.07972222222220.358665181026997259.517029101344
Trimmed Mean ( 19 / 24 )93.06647058823530.347396448966501267.897011800513
Trimmed Mean ( 20 / 24 )93.0656250.337451292034818275.789801955767
Trimmed Mean ( 21 / 24 )93.06733333333330.325356014849069286.047680343352
Trimmed Mean ( 22 / 24 )93.08178571428570.312752354645583297.621374648858
Trimmed Mean ( 23 / 24 )93.10346153846150.303409315970607306.857623143915
Trimmed Mean ( 24 / 24 )93.11541666666670.295128919979409315.507598080063
Median92.975
Midrange96.13
Midmean - Weighted Average at Xnp92.9867567567567
Midmean - Weighted Average at X(n+1)p93.0797222222222
Midmean - Empirical Distribution Function92.9867567567567
Midmean - Empirical Distribution Function - Averaging93.0797222222222
Midmean - Empirical Distribution Function - Interpolation93.0797222222222
Midmean - Closest Observation92.9867567567567
Midmean - True Basic - Statistics Graphics Toolkit93.0797222222222
Midmean - MS Excel (old versions)93.0965789473684
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 93.61625 & 0.597470196135299 & 156.687732050153 \tabularnewline
Geometric Mean & 93.4831857082099 &  &  \tabularnewline
Harmonic Mean & 93.3523621929925 &  &  \tabularnewline
Quadratic Mean & 93.7515182765947 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 93.6188888888889 & 0.593391210039065 & 157.769254591293 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 93.5894444444445 & 0.577392548685332 & 162.089802955613 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 93.4294444444445 & 0.534460658950609 & 174.810704735292 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 93.4172222222222 & 0.528425378980897 & 176.78413251533 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 93.41375 & 0.526913438261151 & 177.284812299097 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 93.48375 & 0.493926589328353 & 189.266486194072 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 93.4759722222222 & 0.480660517260345 & 194.473997479581 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 93.4826388888889 & 0.478885557184708 & 195.208724686663 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 93.4576388888889 & 0.469691383587079 & 198.976694388438 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 93.4298611111111 & 0.464254180565725 & 201.247215474205 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 93.3855555555556 & 0.447588473558379 & 208.641555965751 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 93.3688888888889 & 0.442093670614763 & 211.197072238226 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 93.4140277777778 & 0.421289410731822 & 221.733623960565 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 93.44125 & 0.416246780805929 & 224.485219607178 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 93.41625 & 0.398152936025306 & 234.624039025202 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 93.2918055555556 & 0.37427066929734 & 249.262935112448 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 93.2398611111111 & 0.36280707101271 & 256.995710835649 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 93.1923611111111 & 0.354188468981267 & 263.115175316563 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 93.0736111111111 & 0.33152858294997 & 280.740834720596 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 93.0513888888889 & 0.322078193149076 & 288.909311056087 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 92.9493055555556 & 0.303884818698729 & 305.870184478368 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 92.9095833333333 & 0.273349538445251 & 339.892958524026 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 93.0118055555556 & 0.253910521002225 & 366.317256915638 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 92.9518055555556 & 0.243444354246692 & 381.81951618136 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 93.5444285714286 & 0.567503363630067 & 164.835020488806 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 93.4655882352941 & 0.536277465364209 & 174.285876755641 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 93.3980303030303 & 0.509223972856078 & 183.412477184038 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 93.38625 & 0.497132327047073 & 187.849884063479 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 93.3772580645161 & 0.484750486137362 & 192.629529489644 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 93.3685 & 0.47017437713603 & 198.582705779789 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 93.3446551724138 & 0.461770457004041 & 202.145143234222 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 93.3205357142857 & 0.454672739425632 & 205.247703726802 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 93.2935185185185 & 0.446075922551042 & 209.142690295829 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 93.2682692307692 & 0.43732921434084 & 213.267868169628 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 93.245 & 0.42739813203301 & 218.168946028052 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 93.2258333333333 & 0.418423547815405 & 222.802549761042 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 93.2071739130435 & 0.407947692848996 & 228.478247449103 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 93.1811363636364 & 0.398817122023545 & 233.643771086978 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 93.1492857142857 & 0.387651793783837 & 240.291125200437 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 93.11725 & 0.376909155126204 & 247.054890372246 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 93.0965789473684 & 0.368145611830522 & 252.879773534353 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 93.0797222222222 & 0.358665181026997 & 259.517029101344 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 93.0664705882353 & 0.347396448966501 & 267.897011800513 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 93.065625 & 0.337451292034818 & 275.789801955767 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 93.0673333333333 & 0.325356014849069 & 286.047680343352 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 93.0817857142857 & 0.312752354645583 & 297.621374648858 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 93.1034615384615 & 0.303409315970607 & 306.857623143915 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 93.1154166666667 & 0.295128919979409 & 315.507598080063 \tabularnewline
Median & 92.975 &  &  \tabularnewline
Midrange & 96.13 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 92.9867567567567 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 93.0797222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 92.9867567567567 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 93.0797222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 93.0797222222222 &  &  \tabularnewline
Midmean - Closest Observation & 92.9867567567567 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 93.0797222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 93.0965789473684 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282175&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]93.61625[/C][C]0.597470196135299[/C][C]156.687732050153[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]93.4831857082099[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]93.3523621929925[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]93.7515182765947[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]93.6188888888889[/C][C]0.593391210039065[/C][C]157.769254591293[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]93.5894444444445[/C][C]0.577392548685332[/C][C]162.089802955613[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]93.4294444444445[/C][C]0.534460658950609[/C][C]174.810704735292[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]93.4172222222222[/C][C]0.528425378980897[/C][C]176.78413251533[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]93.41375[/C][C]0.526913438261151[/C][C]177.284812299097[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]93.48375[/C][C]0.493926589328353[/C][C]189.266486194072[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]93.4759722222222[/C][C]0.480660517260345[/C][C]194.473997479581[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]93.4826388888889[/C][C]0.478885557184708[/C][C]195.208724686663[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]93.4576388888889[/C][C]0.469691383587079[/C][C]198.976694388438[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]93.4298611111111[/C][C]0.464254180565725[/C][C]201.247215474205[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]93.3855555555556[/C][C]0.447588473558379[/C][C]208.641555965751[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]93.3688888888889[/C][C]0.442093670614763[/C][C]211.197072238226[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]93.4140277777778[/C][C]0.421289410731822[/C][C]221.733623960565[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]93.44125[/C][C]0.416246780805929[/C][C]224.485219607178[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]93.41625[/C][C]0.398152936025306[/C][C]234.624039025202[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]93.2918055555556[/C][C]0.37427066929734[/C][C]249.262935112448[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]93.2398611111111[/C][C]0.36280707101271[/C][C]256.995710835649[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]93.1923611111111[/C][C]0.354188468981267[/C][C]263.115175316563[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]93.0736111111111[/C][C]0.33152858294997[/C][C]280.740834720596[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]93.0513888888889[/C][C]0.322078193149076[/C][C]288.909311056087[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]92.9493055555556[/C][C]0.303884818698729[/C][C]305.870184478368[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]92.9095833333333[/C][C]0.273349538445251[/C][C]339.892958524026[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]93.0118055555556[/C][C]0.253910521002225[/C][C]366.317256915638[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]92.9518055555556[/C][C]0.243444354246692[/C][C]381.81951618136[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]93.5444285714286[/C][C]0.567503363630067[/C][C]164.835020488806[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]93.4655882352941[/C][C]0.536277465364209[/C][C]174.285876755641[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]93.3980303030303[/C][C]0.509223972856078[/C][C]183.412477184038[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]93.38625[/C][C]0.497132327047073[/C][C]187.849884063479[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]93.3772580645161[/C][C]0.484750486137362[/C][C]192.629529489644[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]93.3685[/C][C]0.47017437713603[/C][C]198.582705779789[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]93.3446551724138[/C][C]0.461770457004041[/C][C]202.145143234222[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]93.3205357142857[/C][C]0.454672739425632[/C][C]205.247703726802[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]93.2935185185185[/C][C]0.446075922551042[/C][C]209.142690295829[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]93.2682692307692[/C][C]0.43732921434084[/C][C]213.267868169628[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]93.245[/C][C]0.42739813203301[/C][C]218.168946028052[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]93.2258333333333[/C][C]0.418423547815405[/C][C]222.802549761042[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]93.2071739130435[/C][C]0.407947692848996[/C][C]228.478247449103[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]93.1811363636364[/C][C]0.398817122023545[/C][C]233.643771086978[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]93.1492857142857[/C][C]0.387651793783837[/C][C]240.291125200437[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]93.11725[/C][C]0.376909155126204[/C][C]247.054890372246[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]93.0965789473684[/C][C]0.368145611830522[/C][C]252.879773534353[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]93.0797222222222[/C][C]0.358665181026997[/C][C]259.517029101344[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]93.0664705882353[/C][C]0.347396448966501[/C][C]267.897011800513[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]93.065625[/C][C]0.337451292034818[/C][C]275.789801955767[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]93.0673333333333[/C][C]0.325356014849069[/C][C]286.047680343352[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]93.0817857142857[/C][C]0.312752354645583[/C][C]297.621374648858[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]93.1034615384615[/C][C]0.303409315970607[/C][C]306.857623143915[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]93.1154166666667[/C][C]0.295128919979409[/C][C]315.507598080063[/C][/ROW]
[ROW][C]Median[/C][C]92.975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]96.13[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]92.9867567567567[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]93.0797222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]92.9867567567567[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]93.0797222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]93.0797222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]92.9867567567567[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]93.0797222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]93.0965789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282175&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282175&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean93.616250.597470196135299156.687732050153
Geometric Mean93.4831857082099
Harmonic Mean93.3523621929925
Quadratic Mean93.7515182765947
Winsorized Mean ( 1 / 24 )93.61888888888890.593391210039065157.769254591293
Winsorized Mean ( 2 / 24 )93.58944444444450.577392548685332162.089802955613
Winsorized Mean ( 3 / 24 )93.42944444444450.534460658950609174.810704735292
Winsorized Mean ( 4 / 24 )93.41722222222220.528425378980897176.78413251533
Winsorized Mean ( 5 / 24 )93.413750.526913438261151177.284812299097
Winsorized Mean ( 6 / 24 )93.483750.493926589328353189.266486194072
Winsorized Mean ( 7 / 24 )93.47597222222220.480660517260345194.473997479581
Winsorized Mean ( 8 / 24 )93.48263888888890.478885557184708195.208724686663
Winsorized Mean ( 9 / 24 )93.45763888888890.469691383587079198.976694388438
Winsorized Mean ( 10 / 24 )93.42986111111110.464254180565725201.247215474205
Winsorized Mean ( 11 / 24 )93.38555555555560.447588473558379208.641555965751
Winsorized Mean ( 12 / 24 )93.36888888888890.442093670614763211.197072238226
Winsorized Mean ( 13 / 24 )93.41402777777780.421289410731822221.733623960565
Winsorized Mean ( 14 / 24 )93.441250.416246780805929224.485219607178
Winsorized Mean ( 15 / 24 )93.416250.398152936025306234.624039025202
Winsorized Mean ( 16 / 24 )93.29180555555560.37427066929734249.262935112448
Winsorized Mean ( 17 / 24 )93.23986111111110.36280707101271256.995710835649
Winsorized Mean ( 18 / 24 )93.19236111111110.354188468981267263.115175316563
Winsorized Mean ( 19 / 24 )93.07361111111110.33152858294997280.740834720596
Winsorized Mean ( 20 / 24 )93.05138888888890.322078193149076288.909311056087
Winsorized Mean ( 21 / 24 )92.94930555555560.303884818698729305.870184478368
Winsorized Mean ( 22 / 24 )92.90958333333330.273349538445251339.892958524026
Winsorized Mean ( 23 / 24 )93.01180555555560.253910521002225366.317256915638
Winsorized Mean ( 24 / 24 )92.95180555555560.243444354246692381.81951618136
Trimmed Mean ( 1 / 24 )93.54442857142860.567503363630067164.835020488806
Trimmed Mean ( 2 / 24 )93.46558823529410.536277465364209174.285876755641
Trimmed Mean ( 3 / 24 )93.39803030303030.509223972856078183.412477184038
Trimmed Mean ( 4 / 24 )93.386250.497132327047073187.849884063479
Trimmed Mean ( 5 / 24 )93.37725806451610.484750486137362192.629529489644
Trimmed Mean ( 6 / 24 )93.36850.47017437713603198.582705779789
Trimmed Mean ( 7 / 24 )93.34465517241380.461770457004041202.145143234222
Trimmed Mean ( 8 / 24 )93.32053571428570.454672739425632205.247703726802
Trimmed Mean ( 9 / 24 )93.29351851851850.446075922551042209.142690295829
Trimmed Mean ( 10 / 24 )93.26826923076920.43732921434084213.267868169628
Trimmed Mean ( 11 / 24 )93.2450.42739813203301218.168946028052
Trimmed Mean ( 12 / 24 )93.22583333333330.418423547815405222.802549761042
Trimmed Mean ( 13 / 24 )93.20717391304350.407947692848996228.478247449103
Trimmed Mean ( 14 / 24 )93.18113636363640.398817122023545233.643771086978
Trimmed Mean ( 15 / 24 )93.14928571428570.387651793783837240.291125200437
Trimmed Mean ( 16 / 24 )93.117250.376909155126204247.054890372246
Trimmed Mean ( 17 / 24 )93.09657894736840.368145611830522252.879773534353
Trimmed Mean ( 18 / 24 )93.07972222222220.358665181026997259.517029101344
Trimmed Mean ( 19 / 24 )93.06647058823530.347396448966501267.897011800513
Trimmed Mean ( 20 / 24 )93.0656250.337451292034818275.789801955767
Trimmed Mean ( 21 / 24 )93.06733333333330.325356014849069286.047680343352
Trimmed Mean ( 22 / 24 )93.08178571428570.312752354645583297.621374648858
Trimmed Mean ( 23 / 24 )93.10346153846150.303409315970607306.857623143915
Trimmed Mean ( 24 / 24 )93.11541666666670.295128919979409315.507598080063
Median92.975
Midrange96.13
Midmean - Weighted Average at Xnp92.9867567567567
Midmean - Weighted Average at X(n+1)p93.0797222222222
Midmean - Empirical Distribution Function92.9867567567567
Midmean - Empirical Distribution Function - Averaging93.0797222222222
Midmean - Empirical Distribution Function - Interpolation93.0797222222222
Midmean - Closest Observation92.9867567567567
Midmean - True Basic - Statistics Graphics Toolkit93.0797222222222
Midmean - MS Excel (old versions)93.0965789473684
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')